1. Tardigrade
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  3. Physics
  4. In the potentiometer arrangement shown, the driving cell A has emf ε and internal resistance r. The emf of the cell. B is (ε/2) and internal resistance 2 r. The potentiometer wire C D is 100 cm long. If balance is obtained with length C J=l, then

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Q. In the potentiometer arrangement shown, the driving cell $A$ has emf $\varepsilon$ and internal resistance $r$. The emf of the cell. $B$ is $\frac{\varepsilon}{2}$ and internal resistance $2 r$. The potentiometer wire $C D$ is $100\, cm$ long. If balance is obtained with length $C J=l$, thenPhysics Question Image

Current Electricity

Solution:

As potential gradient $k$ in the potentiometer wire will be less than $(\varepsilon / 100)( V / cm )$ because of presence of $r$, so for the battery of emf $(\varepsilon / 2)$ the balance point $l$ will be greater than $50\, cm$ as shown.
$l=\frac{\varepsilon / 2}{k( < \varepsilon / 100)} \Rightarrow l > 50 cm$